In [1]}, the Orlicz projection body \(\Pi _{\phi }K\) of \(K\in \mathcal {K}^n_o\)  is defined as the body whose support function is given by
\(h_{\Pi _{\phi }K}(u)=\inf \left\lbrace \lambda >0:\int _{\partial K}\phi \left(\frac{u\cdot v_K(y)}{\lambda h_K(v_K(y))}\right)h_K(v_K(y))d\mathcal {H}^{n-1}(y)\le n|K|\right\rbrace .\) 
